Constitutive modeling of the biaxial mechanics of brain white matter.

摘要

It is important to characterize the mechanical behavior of brain tissue to aid in the computational models used for simulated neurosurgery. Due to its anisotropy, it is of particular interest to develop constitutive models of white matter based on experimental data in order to define the material properties in computational models. White matter has been shown to exhibit anisotropic, hyperelastic, and viscoelastic properties. The majority of studies have focused on the shear or compressive properties, while few have tested the tensile properties of the brain. Brain tissue has not previously been tested in a multi-axial loading state, even though in vivo brain tissue is in a constant multi-axial stress state due to fluid pressure, and data from uniaxial experiments do not sufficiently describe multi-axial stresses.;The main objective of this project was to characterize the biaxial tensile behavior of brain white matter via experimentation and constitutive modeling. A biaxial experiment was developed specifically for testing brain tissue. Experiments were performed at a quasi-static loading rate, and an Ogden anisotropic hyperelastic model was derived to fit the data. A structural analysis was performed on biaxially tested specimens to relate the structure to the mechanical behavior. The axonal orientation and distribution were measured via histology, and the axon area fraction was measured via transmission electron microscopy. The measured structural parameters were incorporated into the constitutive model. A probabilistic analysis was performed to compare the uncertainty in the stress predictions between models with and without structural parameters. Finally, dynamic biaxial experiments were performed to characterize the anisotropic viscoelastic properties of white matter. Biaxial stress-relaxation experiments were conducted to determine the appropriate form of a viscoelastic model. It was found that the data were accurately modeled by a quasi-linear viscoelastic formulation with an isotropic reduced relaxation tensor and an instantaneous elastic stress defined by an anisotropic Ogden model. Model fits to the stress-relaxation experiments were able to accurately predict the results of dynamic cyclic experiments.;The resulting constitutive models from this project build upon previous models of brain white matter mechanics to include biaxial interactions and structural relations, thus improving computational model predictions.